The emergence of human-transmissible H5N1 avian influenza viruses poses a major pandemic threat. H5N1 viruses are thought to be highly genetically diverse both among and within hosts; however, the effects of this diversity on viral replication and transmission are poorly understood. Here we use deep sequencing to investigate the impact of within-host viral variation on adaptation and transmission of H5N1 viruses in ferrets. We show that, although within-host genetic diversity in haemagglutinin (HA) increases during replication in inoculated ferrets, HA diversity is dramatically reduced upon respiratory droplet transmission, in which infection is established by only 1-2 distinct HA segments from a diverse source virus population in transmitting animals. Moreover, minor HA variants present in as little as 5.9% of viruses within the source animal become dominant in ferrets infected via respiratory droplets. These findings demonstrate that selective pressures acting during influenza virus transmission among mammals impose a significant bottleneck.